Flat-Bands on Partial Line Graphs -- Systematic Method for Generating Flat-Band Lattice Structures

TL;DR

This paper presents a systematic method to generate lattice structures called partial line graphs, which produce flat energy bands in tight-binding models, applicable to 2D and 3D systems, aiding material synthesis.

Contribution

The paper introduces a novel, systematic approach for constructing partial line graphs that reliably produce flat energy bands in tight-binding models.

Findings

Applicable to 2D and 3D lattice systems

Provides a flexible framework for flat-band material design

Demonstrates examples with square and cubic lattices

Abstract

We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied to two- and three-dimensional systems. We show examples of partial line graphs of square and cubic lattices. The method is useful in providing a guideline for synthesizing materials with flat energy bands, since the tight-binding models on the partial line graphs provide us a large room for modification, maintaining the flat energy dispersions.